Start Limitations
At the basic level all turbine engines start the same way - you spin them up (using an electric motor, an air source, whatever) until they are going fast enough that there is a stable airflow through the engine in the right direction, then you introduce fuel and ignite it which accelerates the engine to the normal idle state.
The design of the starting cycle is a compromise between the weight and cost of the starter (which may be an APU, a battery and starter motor, whatever) and the ability of the engine to start reliably and at a reasonable temperature. The temperature is the most obvious constraint, because all turbine engines are also effectively air cooled - if you light them up when the RPM is too low, then the innards will overheat.
Onto your specific example - the PT6. The PT6 invariably uses a straighforward electric starter motor to spin it up for starting. In the absence of ground power, starting the first engine is always a battery start. In some aircraft types, starting the second engine can then be helped by power from the first engine alternator. Spinning up a turbine engine for the start takes a lot of energy, and in either case, after the start sequence you will find that (1) the starter motors are seriously hot and (2) the battery will have taken a beating. Most PT6 aircraft I am familiar with (I should say that list does not include the Twotter) have a start limitation, such as three start sequences per hour, or something similar. This phenomenon is not a PT6 feature - the smaller Citations have similar limitations - it is a feature of starting a turbine engine on a battery.
The limitation is therefore - how long was it since I last started the engines? No matter how fast the turn-around, if it comes at the end of a 90 minute flight, it is unlikely to be an issue (EasyJet, Ryanair, etc). Twotter pilots like your friend often find themselves doing very short trips - a 20 minute flight would be quite reasonable. A 20 minute flight to a short turn around could face the pilot with a second engine start sequence less than 30 minutes after the previous one. Hence, tricks to avoid doing the whole sequence are common.
As an aside, at small airfields you often see piston aircraft start up, taxy to the fuel pumps, shut down, refuel, start up, taxy to the parking area, shut down, load passengers, start up, and depart. You'll never see a turbine aircraft do that!